We consider a quantum system A U B made up of degrees of freedom that can be
partitioned into spatially disjoint regions A and B. When the full system is in
a pure state in which regions A and B are entangled, the quantum mechanics of
region A described without reference to its complement is traditionally assumed
to require a reduced density matrix on A. While this is certainly true as an
exact matter, we argue that under many interesting circumstances expectation
values of typical operators anywhere inside A can be computed from a suitable
pure state on A alone, with a controlled error. We use insights from quantum
statistical mechanics - specifically the eigenstate thermalization hypothesis
(ETH) - to argue for the existence of such "representative states".
Description
Eigenstate Thermalization and Representative States on Subsystems
%0 Generic
%1 khemani2014eigenstate
%A Khemani, Vedika
%A Chandran, Anushya
%A Kim, Hyungwon
%A Sondhi, S. L.
%D 2014
%K interesting
%T Eigenstate Thermalization and Representative States on Subsystems
%U http://arxiv.org/abs/1406.4863
%X We consider a quantum system A U B made up of degrees of freedom that can be
partitioned into spatially disjoint regions A and B. When the full system is in
a pure state in which regions A and B are entangled, the quantum mechanics of
region A described without reference to its complement is traditionally assumed
to require a reduced density matrix on A. While this is certainly true as an
exact matter, we argue that under many interesting circumstances expectation
values of typical operators anywhere inside A can be computed from a suitable
pure state on A alone, with a controlled error. We use insights from quantum
statistical mechanics - specifically the eigenstate thermalization hypothesis
(ETH) - to argue for the existence of such "representative states".
@misc{khemani2014eigenstate,
abstract = {We consider a quantum system A U B made up of degrees of freedom that can be
partitioned into spatially disjoint regions A and B. When the full system is in
a pure state in which regions A and B are entangled, the quantum mechanics of
region A described without reference to its complement is traditionally assumed
to require a reduced density matrix on A. While this is certainly true as an
exact matter, we argue that under many interesting circumstances expectation
values of typical operators anywhere inside A can be computed from a suitable
pure state on A alone, with a controlled error. We use insights from quantum
statistical mechanics - specifically the eigenstate thermalization hypothesis
(ETH) - to argue for the existence of such "representative states".},
added-at = {2014-06-20T14:25:57.000+0200},
author = {Khemani, Vedika and Chandran, Anushya and Kim, Hyungwon and Sondhi, S. L.},
biburl = {https://www.bibsonomy.org/bibtex/2a3ef54e42f989361431c95672cd2a3a8/scavgf},
description = {Eigenstate Thermalization and Representative States on Subsystems},
interhash = {2233c5f50dc7e3c3f4fd4b50d7457f52},
intrahash = {a3ef54e42f989361431c95672cd2a3a8},
keywords = {interesting},
note = {cite arxiv:1406.4863},
timestamp = {2014-06-20T14:25:57.000+0200},
title = {Eigenstate Thermalization and Representative States on Subsystems},
url = {http://arxiv.org/abs/1406.4863},
year = 2014
}